Beta Story DONT READ
by liteMARGARITA
Summary: DONT Read


Social Class Divisions and Troubles in British Society

In the movie, _Master and Commander: The Far Side of the World_, the social class divisions and the difficulty of the ability permeate through social barriers are shown through the crew. The social class divisions are shown during meal time. The officers eat fine food, served on silver platters, served by the working class. The crew does not eat this food, and instead hang out on the deck or in their quarters, singing and drinking. The officers on the other hand, sit in the dining hall and tell jokes and stories, while having a fine meal. The ways the crew and officers are treated for wounds demonstrates another social class division between the officers and crew. The officers are treated in the medical quarter with a piece of leather to bite on for the pain. The crew, however, is treated on the deck with nothing to bite on, while the doctor performs his duties, as shown when the doctor, Stephen Maturin, performs surgery on Joe, a shipman. Another social class division that is shown in the movie is before they attack the _Acheron_, the Captain, Jack Aubrey, appoints the young midshipman Blakeney to both command the ship after the attack and lead his own gunboat. Despite being much younger than the crew and far less experienced, Blakeney is given command. The difficulty to permeate between social barriers is shown by how midshipman Hollom and the crew do not get along. The crew is disrespectful towards Hollom because he is nice to them and not a respectable leader. One of the crew calls him the cause of the ships misfortunes due to circumstances beyond his control. This leads to him drowning himself. The social class divisions in British society are shown throughout the film along with difficulty of permeating through the social barriers in British society. One Scientific discovery often leads to another one, like how Isaac Newton's telescope was an improvement of the reflecting telescope. Although gravity is what most modern people know Sir Isaac Newton for, he had many more achievements besides gravity. Isaac Newton had many important accomplishments in mathematics, including his equations for his laws of physics. Newton's invention of differential calculus allowed him to create his equations. Another accomplishment of Newton was the advancement in the study of optical physics. Newton's most famous accomplishments come in mechanical physics, which he studied after optical physics. All of Newton's work on fields of motion and gravity, including his synthesis, can be found in his _Philosophiae Naturalis Principia Mathematica._ Sir Isaac Newton impacted modern science by setting the basis that science builds upon itself with each discovery leading to a new discovery.

Of Newton's mathematical achievements, he had his most important achievements in equations and theorems. Newton's equations are the mathematical equations for his three laws of motion and the equation for figuring out the force of gravity on an object. Newton's theorem is the binomial theorem. The binomial theorem allows one to take the sum of two integer numbers raised to a power and figure out the answer with only one line of mathematical code. Newton figured out his first law's mathematical equation, ⅀F=0⇒dv/d_t_=0, by observing that planets move in orbit without crashing to the ground, and by watching an apple fall out of a tree. This equation means an object at rest will stay at rest or will continue to stay in motion in a straight line at a constant speed unless an outside force acts upon the object (Allan 33). Newton's equation for the second of the three laws of motion is a=F/_m_. Newton figured out what this laws means by seeing that unequal forces acting on an object created acceleration. What this means is that he observed something like a push would be needed to get an object in motion, otherwise the object would stay at rest continually, which is his first law of motion. Once the push is applied however, the object will accelerate in that direction and at the rate that depends on the object's mass and on the size of the force (Allan 33). Newton's last equation, his equation for the force of gravity on an object is F=G(m1m2/r^2). This equation means that any two objects in the universe attract each other with the resulting force equaling the force of gravity, which equals a force that is directly proportional to the masses times each other and inversely proportional to the distance between the two objects squared. Newton figured out the equation for the gravitational force on an object by observing that if dropped from high enough, two objects even if they do not have the same mass, will hit the ground at the same time. Newton's equations help to prove his laws of motion and the law of universal gravitation by providing mathematical explanation and proof that his laws are correct. With mathematical proof that his equations and ideas work, one can expand upon his equations and apply them to other areas.

Newton's other achievement in mathematics was fluxions and differential calculus. Although he called them "fluxions", they are known today as "derivatives" and are essential in modern calculus (Steele 29). A derivative is the slope of a graph. Calculus "combines arithmetic with geometry and algebra, to compare the rate of change in one thing to the rate of change in another" (Steele 29). There are two types of calculus, differential and integral. While Sir Isaac Newton came up with differential calculus and derivatives, he did not invent integral calculus. Instead, Newton made the discovery of the Fundamental Theorem of Calculus, which states that derivatives and integrals are inverse processes (Calculus). Newton created differential calculus because he wanted to be able to prove the law of universal gravitation, and the strength of mathematics at the time was not strong enough for him to do so. More specifically, Newton "wanted to be able to calculate velocities and accelerations at any point along the path of motion" (Calculus). This takes the form of a curved line and this curved line is known as a derivative. Newton created differential equations as well. A differential equation is "an equation that contains derivatives or instantaneous rates of change" (Calculus). These equations can be used to describe changing phenomena (Calculus), like the three laws of motion. All three laws of motion are differential equations. In "On the Quadrature of Curves", Newton published his findings for derivatives. While Isaac Newton used differential calculus to determine the laws of motion and the law of gravity, it is used today by biologists to determine the rate growth of bacteria when variables such as food and temperature are changed. Another use of differential calculus is credit card companies use differential calculus to figure out the minimum payment due on a credit card statement by considering factors including fluctuating interest rates and a changing available bank balance. Differential calculus can also be used by graphics artists. The graphic artists will use differential calculus to see how different 3-D models will behave when put under swiftly changing conditions. Differential calculus has many uses that contribute to both science and other fields.

Even though his discoveries and accomplishments in mechanical physics are what Isaac Newton is most known for, he had many significant discoveries in optics as well. Optics is a branch of physics that deals with qualities of light, such as its behavior and properties. Included the study of optics is how light interacts with matter and instruments that build or detect light. One of Newton's most important discoveries regarding optics was his work about the spectrum. The spectrum are the "colors into which white light breaks down when passed through a prism" (Allan 47). Newton used a prism and held in sunlight and observed the spectrum. Newton then tried to use another prism to divide up individual colors of the spectrum, but it did not work. Newton's Color Theory is based off of his observation. His color theory states that light that has already been defracted will not change color after being put through a prism again. This led Newton to very important conclusion that "the white light of the sun was a different kind of light from the other colors, because it was a mixture of all of them" (Allan 15). Newton's work on the spectrum affected the development of spectroscopy, which is very important to modern astronomy. Spectroscopy is the science of the interactions that take place between radiation and matter. Spectroscopy can be used to find information about the chemical composition of a star, the temperature of a star, the speed of a star, and how strong a star's magnetic field is, by studying the spectra made by spectra are the individual bands of color from a spectrum. The information about stars is very useful to NASA, the National Aeronautics and Space Administration. Even though Newton did not invent the reflecting telescope, a telescope using mirrors, he greatly improved upon it (Steele 40). Newton's improvement was to use two mirrors. His telescope had a concave mirror at the back, which bounced the rays of light forward to the smaller second mirror halfway up the tube of the telescope. The second mirror reflected the light to an eyepiece, put at the side of telescope tube rather than at the end of the telescope (Allan 27). His telescope magnified objects forty times larger than a refracting telescope, the popular form of the telescope at the time, could. This telescope is now known as a Newtonian telescope. Newton published his findings in his book, _Opticks_. One of the main points of _Opticks_, was that Newton agreed with the theory that light is composed of small particles. The Corpuscular theory is the theory that light travels as a stream of particles that are absorbed by the eye (Light). Also included in _Opticks_ are "discussions of volcanoes, electricity, chemical reactions, capillary action, animal structure, [and God]" (Fara 68). Newton's discoveries in optics, the branch of science that studies light and its properties, impact modern science through spectroscopy, his telescope and his book on the topic, _Opticks_.

Newton's most famous achievements are in mechanical physics. Newton's achievements in this field of science include the three laws of motion, also known as Newton's laws, the law for universal gravitation, and Newton's Synthesis. The first of Newton's three laws states that an object at rest will stay at rest and an object in motion will stay in motion unless an outside unbalanced force is acted upon the object. Newton's second law is that force equals an object's mass times the object acceleration. Newton's third law, "commonly known as the law of action and reaction, states that forces always occur in equal and opposite pairs" (Bortz xx). The law for universal gravitation is that any two objects in the universe attract each other with a force that is directly related to the product of their masses, and inversely related to their distance from each other squared. An example of Newton's first law is if a spaceship were to just drift along in space, it would go on forever and ever, but because the spaceship is acted upon by a planet's gravity, the space ship does not move continuously, instead it moves towards the planet that is acting upon it. An example of Newton's second law is a rocket launching from the launch pad towards space. The object moves up because the rocket's boosters are propelling the rocket that way and as it is moving up, the rocket's mass changes. Mass is the amount of matter in an object, and as the rocket is moving up, fuel is spent so the mass decreases. The force of the boosters however does not decrease, and it is this that causes increasing acceleration. An example of Newton's third law is how the Moon and the Earth interact with each other. While the Earth's gravitational field holds the Moon in its orbit, the Moon's gravity pulls back on the Earth with equal strength (Bortz xx). These laws of motion have been used by others to explain why their ideas would work such as a rocket.

Newton's_ Philosophiae Naturalis Principia Mathematica_, more commonly called _Principia_, included differential and integral calculus, three general laws of motion, universal gravitation, and more (Wiggins). _Principia_ expressed in detail how objects moved on Earth and how planets orbited in space. The most important part of _Principia _is that the book gave a mathematical foundation that could be used to test Newton's ideas. These laws provide the basis for classical mechanics and celestial mechanics. Classical mechanics describes how objects that are not microscopic, such as machine parts, planets, rockets, bullets, etc move. Celestial mechanics is the area of astronomy where Newton's laws of motions are applied to objects in the sky (Celestial). Newton's synthesis helped to explain how the universe works. Newton uses his laws of motion and gravity to explain why celestial bodies, such as the moon and stars, travel in the paths they do (Celestial). The mathematically proven laws of gravitational force and motion are why his synthesis work. Due to Newton's synthesis, questioning of the church and Bible was increased because Newton provided a mathematically proven explanation of the universe, which contradicted what the Church believed, and so others thought that the church may have been wrong about other subjects as well. Newton's discoveries in mechanical physics have helped to form the basis for modern science due to the laws of motion and his synthesis.

Sir Isaac Newton impacted modern science through his discoveries in math and science, which led to more discoveries in those fields and others. Newton's discoveries in math helped impact modern science because they provided mathematical proof that his equations and laws of motion worked. Newton's discoveries in optics helped impact modern science by helping modern organizations such as NASA. Newton's discoveries in physics have impacted science by proving that the church was wrong about some of their beliefs, such as the movement of celestial bodies. This led to increased questioning of various subjects and so more knowledge due to more experimentation. Also, Newton showed that science is enduring and that one topic builds upon another topic, like how his three laws of motion then became the basis for classical and celestial mechanics today. For example, Newton's work in celestial mechanics was modified by Albert Einstein (Celestial). Science advancements not only build on each other, but also expand into other fields as Newton's achievements have shown.

One Scientific discovery often leads to another one, like how Isaac Newton's telescope was an improvement of the reflecting telescope. Although gravity is what most modern people know Sir Isaac Newton for, he had many more achievements besides gravity. Isaac Newton had many important accomplishments in mathematics, including his equations for his laws of physics. Newton's invention of differential calculus allowed him to create his equations. Another accomplishment of Newton was the advancement in the study of optical physics. Newton's most famous accomplishments come in mechanical physics, which he studied after optical physics. All of Newton's work on fields of motion and gravity, including his synthesis, can be found in his _Philosophiae Naturalis Principia Mathematica._ Sir Isaac Newton impacted modern science by setting the basis that science builds upon itself with each discovery leading to a new discovery.

Of Newton's mathematical achievements, he had his most important achievements in equations and theorems. Newton's equations are the mathematical equations for his three laws of motion and the equation for figuring out the force of gravity on an object. Newton's theorem is the binomial theorem. The binomial theorem allows one to take the sum of two integer numbers raised to a power and figure out the answer with only one line of mathematical code. Newton figured out his first law's mathematical equation, ⅀F=0⇒dv/d_t_=0, by observing that planets move in orbit without crashing to the ground, and by watching an apple fall out of a tree. This equation means an object at rest will stay at rest or will continue to stay in motion in a straight line at a constant speed unless an outside force acts upon the object (Allan 33). Newton's equation for the second of the three laws of motion is a=F/_m_. Newton figured out what this laws means by seeing that unequal forces acting on an object created acceleration. What this means is that he observed something like a push would be needed to get an object in motion, otherwise the object would stay at rest continually, which is his first law of motion. Once the push is applied however, the object will accelerate in that direction and at the rate that depends on the object's mass and on the size of the force (Allan 33). Newton's last equation, his equation for the force of gravity on an object is F=G(m1m2/r^2). This equation means that any two objects in the universe attract each other with the resulting force equaling the force of gravity, which equals a force that is directly proportional to the masses times each other and inversely proportional to the distance between the two objects squared. Newton figured out the equation for the gravitational force on an object by observing that if dropped from high enough, two objects even if they do not have the same mass, will hit the ground at the same time. Newton's equations help to prove his laws of motion and the law of universal gravitation by providing mathematical explanation and proof that his laws are correct. With mathematical proof that his equations and ideas work, one can expand upon his equations and apply them to other areas.

Newton's other achievement in mathematics was fluxions and differential calculus. Although he called them "fluxions", they are known today as "derivatives" and are essential in modern calculus (Steele 29). A derivative is the slope of a graph. Calculus "combines arithmetic with geometry and algebra, to compare the rate of change in one thing to the rate of change in another" (Steele 29). There are two types of calculus, differential and integral. While Sir Isaac Newton came up with differential calculus and derivatives, he did not invent integral calculus. Instead, Newton made the discovery of the Fundamental Theorem of Calculus, which states that derivatives and integrals are inverse processes (Calculus). Newton created differential calculus because he wanted to be able to prove the law of universal gravitation, and the strength of mathematics at the time was not strong enough for him to do so. More specifically, Newton "wanted to be able to calculate velocities and accelerations at any point along the path of motion" (Calculus). This takes the form of a curved line and this curved line is known as a derivative. Newton created differential equations as well. A differential equation is "an equation that contains derivatives or instantaneous rates of change" (Calculus). These equations can be used to describe changing phenomena (Calculus), like the three laws of motion. All three laws of motion are differential equations. In "On the Quadrature of Curves", Newton published his findings for derivatives. While Isaac Newton used differential calculus to determine the laws of motion and the law of gravity, it is used today by biologists to determine the rate growth of bacteria when variables such as food and temperature are changed. Another use of differential calculus is credit card companies use differential calculus to figure out the minimum payment due on a credit card statement by considering factors including fluctuating interest rates and a changing available bank balance. Differential calculus can also be used by graphics artists. The graphic artists will use differential calculus to see how different 3-D models will behave when put under swiftly changing conditions. Differential calculus has many uses that contribute to both science and other fields.

Even though his discoveries and accomplishments in mechanical physics are what Isaac Newton is most known for, he had many significant discoveries in optics as well. Optics is a branch of physics that deals with qualities of light, such as its behavior and properties. Included the study of optics is how light interacts with matter and instruments that build or detect light. One of Newton's most important discoveries regarding optics was his work about the spectrum. The spectrum are the "colors into which white light breaks down when passed through a prism" (Allan 47). Newton used a prism and held in sunlight and observed the spectrum. Newton then tried to use another prism to divide up individual colors of the spectrum, but it did not work. Newton's Color Theory is based off of his observation. His color theory states that light that has already been defracted will not change color after being put through a prism again. This led Newton to very important conclusion that "the white light of the sun was a different kind of light from the other colors, because it was a mixture of all of them" (Allan 15). Newton's work on the spectrum affected the development of spectroscopy, which is very important to modern astronomy. Spectroscopy is the science of the interactions that take place between radiation and matter. Spectroscopy can be used to find information about the chemical composition of a star, the temperature of a star, the speed of a star, and how strong a star's magnetic field is, by studying the spectra made by spectra are the individual bands of color from a spectrum. The information about stars is very useful to NASA, the National Aeronautics and Space Administration. Even though Newton did not invent the reflecting telescope, a telescope using mirrors, he greatly improved upon it (Steele 40). Newton's improvement was to use two mirrors. His telescope had a concave mirror at the back, which bounced the rays of light forward to the smaller second mirror halfway up the tube of the telescope. The second mirror reflected the light to an eyepiece, put at the side of telescope tube rather than at the end of the telescope (Allan 27). His telescope magnified objects forty times larger than a refracting telescope, the popular form of the telescope at the time, could. This telescope is now known as a Newtonian telescope. Newton published his findings in his book, _Opticks_. One of the main points of _Opticks_, was that Newton agreed with the theory that light is composed of small particles. The Corpuscular theory is the theory that light travels as a stream of particles that are absorbed by the eye (Light). Also included in _Opticks_ are "discussions of volcanoes, electricity, chemical reactions, capillary action, animal structure, [and God]" (Fara 68). Newton's discoveries in optics, the branch of science that studies light and its properties, impact modern science through spectroscopy, his telescope and his book on the topic, _Opticks_.

Newton's most famous achievements are in mechanical physics. Newton's achievements in this field of science include the three laws of motion, also known as Newton's laws, the law for universal gravitation, and Newton's Synthesis. The first of Newton's three laws states that an object at rest will stay at rest and an object in motion will stay in motion unless an outside unbalanced force is acted upon the object. Newton's second law is that force equals an object's mass times the object acceleration. Newton's third law, "commonly known as the law of action and reaction, states that forces always occur in equal and opposite pairs" (Bortz xx). The law for universal gravitation is that any two objects in the universe attract each other with a force that is directly related to the product of their masses, and inversely related to their distance from each other squared. An example of Newton's first law is if a spaceship were to just drift along in space, it would go on forever and ever, but because the spaceship is acted upon by a planet's gravity, the space ship does not move continuously, instead it moves towards the planet that is acting upon it. An example of Newton's second law is a rocket launching from the launch pad towards space. The object moves up because the rocket's boosters are propelling the rocket that way and as it is moving up, the rocket's mass changes. Mass is the amount of matter in an object, and as the rocket is moving up, fuel is spent so the mass decreases. The force of the boosters however does not decrease, and it is this that causes increasing acceleration. An example of Newton's third law is how the Moon and the Earth interact with each other. While the Earth's gravitational field holds the Moon in its orbit, the Moon's gravity pulls back on the Earth with equal strength (Bortz xx). These laws of motion have been used by others to explain why their ideas would work such as a rocket.

Newton's_ Philosophiae Naturalis Principia Mathematica_, more commonly called _Principia_, included differential and integral calculus, three general laws of motion, universal gravitation, and more (Wiggins). _Principia_ expressed in detail how objects moved on Earth and how planets orbited in space. The most important part of _Principia _is that the book gave a mathematical foundation that could be used to test Newton's ideas. These laws provide the basis for classical mechanics and celestial mechanics. Classical mechanics describes how objects that are not microscopic, such as machine parts, planets, rockets, bullets, etc move. Celestial mechanics is the area of astronomy where Newton's laws of motions are applied to objects in the sky (Celestial). Newton's synthesis helped to explain how the universe works. Newton uses his laws of motion and gravity to explain why celestial bodies, such as the moon and stars, travel in the paths they do (Celestial). The mathematically proven laws of gravitational force and motion are why his synthesis work. Due to Newton's synthesis, questioning of the church and Bible was increased because Newton provided a mathematically proven explanation of the universe, which contradicted what the Church believed, and so others thought that the church may have been wrong about other subjects as well. Newton's discoveries in mechanical physics have helped to form the basis for modern science due to the laws of motion and his synthesis.

Sir Isaac Newton impacted modern science through his discoveries in math and science, which led to more discoveries in those fields and others. Newton's discoveries in math helped impact modern science because they provided mathematical proof that his equations and laws of motion worked. Newton's discoveries in optics helped impact modern science by helping modern organizations such as NASA. Newton's discoveries in physics have impacted science by proving that the church was wrong about some of their beliefs, such as the movement of celestial bodies. This led to increased questioning of various subjects and so more knowledge due to more experimentation. Also, Newton showed that science is enduring and that one topic builds upon another topic, like how his three laws of motion then became the basis for classical and celestial mechanics today. For example, Newton's work in celestial mechanics was modified by Albert Einstein (Celestial). Science advancements not only build on each other, but also expand into other fields as Newton's achievements have shown.

One Scientific discovery often leads to another one, like how Isaac Newton's telescope was an improvement of the reflecting telescope. Although gravity is what most modern people know Sir Isaac Newton for, he had many more achievements besides gravity. Isaac Newton had many important accomplishments in mathematics, including his equations for his laws of physics. Newton's invention of differential calculus allowed him to create his equations. Another accomplishment of Newton was the advancement in the study of optical physics. Newton's most famous accomplishments come in mechanical physics, which he studied after optical physics. All of Newton's work on fields of motion and gravity, including his synthesis, can be found in his _Philosophiae Naturalis Principia Mathematica._ Sir Isaac Newton impacted modern science by setting the basis that science builds upon itself with each discovery leading to a new discovery.

Of Newton's mathematical achievements, he had his most important achievements in equations and theorems. Newton's equations are the mathematical equations for his three laws of motion and the equation for figuring out the force of gravity on an object. Newton's theorem is the binomial theorem. The binomial theorem allows one to take the sum of two integer numbers raised to a power and figure out the answer with only one line of mathematical code. Newton figured out his first law's mathematical equation, ⅀F=0⇒dv/d_t_=0, by observing that planets move in orbit without crashing to the ground, and by watching an apple fall out of a tree. This equation means an object at rest will stay at rest or will continue to stay in motion in a straight line at a constant speed unless an outside force acts upon the object (Allan 33). Newton's equation for the second of the three laws of motion is a=F/_m_. Newton figured out what this laws means by seeing that unequal forces acting on an object created acceleration. What this means is that he observed something like a push would be needed to get an object in motion, otherwise the object would stay at rest continually, which is his first law of motion. Once the push is applied however, the object will accelerate in that direction and at the rate that depends on the object's mass and on the size of the force (Allan 33). Newton's last equation, his equation for the force of gravity on an object is F=G(m1m2/r^2). This equation means that any two objects in the universe attract each other with the resulting force equaling the force of gravity, which equals a force that is directly proportional to the masses times each other and inversely proportional to the distance between the two objects squared. Newton figured out the equation for the gravitational force on an object by observing that if dropped from high enough, two objects even if they do not have the same mass, will hit the ground at the same time. Newton's equations help to prove his laws of motion and the law of universal gravitation by providing mathematical explanation and proof that his laws are correct. With mathematical proof that his equations and ideas work, one can expand upon his equations and apply them to other areas.

Newton's other achievement in mathematics was fluxions and differential calculus. Although he called them "fluxions", they are known today as "derivatives" and are essential in modern calculus (Steele 29). A derivative is the slope of a graph. Calculus "combines arithmetic with geometry and algebra, to compare the rate of change in one thing to the rate of change in another" (Steele 29). There are two types of calculus, differential and integral. While Sir Isaac Newton came up with differential calculus and derivatives, he did not invent integral calculus. Instead, Newton made the discovery of the Fundamental Theorem of Calculus, which states that derivatives and integrals are inverse processes (Calculus). Newton created differential calculus because he wanted to be able to prove the law of universal gravitation, and the strength of mathematics at the time was not strong enough for him to do so. More specifically, Newton "wanted to be able to calculate velocities and accelerations at any point along the path of motion" (Calculus). This takes the form of a curved line and this curved line is known as a derivative. Newton created differential equations as well. A differential equation is "an equation that contains derivatives or instantaneous rates of change" (Calculus). These equations can be used to describe changing phenomena (Calculus), like the three laws of motion. All three laws of motion are differential equations. In "On the Quadrature of Curves", Newton published his findings for derivatives. While Isaac Newton used differential calculus to determine the laws of motion and the law of gravity, it is used today by biologists to determine the rate growth of bacteria when variables such as food and temperature are changed. Another use of differential calculus is credit card companies use differential calculus to figure out the minimum payment due on a credit card statement by considering factors including fluctuating interest rates and a changing available bank balance. Differential calculus can also be used by graphics artists. The graphic artists will use differential calculus to see how different 3-D models will behave when put under swiftly changing conditions. Differential calculus has many uses that contribute to both science and other fields.

Even though his discoveries and accomplishments in mechanical physics are what Isaac Newton is most known for, he had many significant discoveries in optics as well. Optics is a branch of physics that deals with qualities of light, such as its behavior and properties. Included the study of optics is how light interacts with matter and instruments that build or detect light. One of Newton's most important discoveries regarding optics was his work about the spectrum. The spectrum are the "colors into which white light breaks down when passed through a prism" (Allan 47). Newton used a prism and held in sunlight and observed the spectrum. Newton then tried to use another prism to divide up individual colors of the spectrum, but it did not work. Newton's Color Theory is based off of his observation. His color theory states that light that has already been defracted will not change color after being put through a prism again. This led Newton to very important conclusion that "the white light of the sun was a different kind of light from the other colors, because it was a mixture of all of them" (Allan 15). Newton's work on the spectrum affected the development of spectroscopy, which is very important to modern astronomy. Spectroscopy is the science of the interactions that take place between radiation and matter. Spectroscopy can be used to find information about the chemical composition of a star, the temperature of a star, the speed of a star, and how strong a star's magnetic field is, by studying the spectra made by spectra are the individual bands of color from a spectrum. The information about stars is very useful to NASA, the National Aeronautics and Space Administration. Even though Newton did not invent the reflecting telescope, a telescope using mirrors, he greatly improved upon it (Steele 40). Newton's improvement was to use two mirrors. His telescope had a concave mirror at the back, which bounced the rays of light forward to the smaller second mirror halfway up the tube of the telescope. The second mirror reflected the light to an eyepiece, put at the side of telescope tube rather than at the end of the telescope (Allan 27). His telescope magnified objects forty times larger than a refracting telescope, the popular form of the telescope at the time, could. This telescope is now known as a Newtonian telescope. Newton published his findings in his book, _Opticks_. One of the main points of _Opticks_, was that Newton agreed with the theory that light is composed of small particles. The Corpuscular theory is the theory that light travels as a stream of particles that are absorbed by the eye (Light). Also included in _Opticks_ are "discussions of volcanoes, electricity, chemical reactions, capillary action, animal structure, [and God]" (Fara 68). Newton's discoveries in optics, the branch of science that studies light and its properties, impact modern science through spectroscopy, his telescope and his book on the topic, _Opticks_.

Newton's most famous achievements are in mechanical physics. Newton's achievements in this field of science include the three laws of motion, also known as Newton's laws, the law for universal gravitation, and Newton's Synthesis. The first of Newton's three laws states that an object at rest will stay at rest and an object in motion will stay in motion unless an outside unbalanced force is acted upon the object. Newton's second law is that force equals an object's mass times the object acceleration. Newton's third law, "commonly known as the law of action and reaction, states that forces always occur in equal and opposite pairs" (Bortz xx). The law for universal gravitation is that any two objects in the universe attract each other with a force that is directly related to the product of their masses, and inversely related to their distance from each other squared. An example of Newton's first law is if a spaceship were to just drift along in space, it would go on forever and ever, but because the spaceship is acted upon by a planet's gravity, the space ship does not move continuously, instead it moves towards the planet that is acting upon it. An example of Newton's second law is a rocket launching from the launch pad towards space. The object moves up because the rocket's boosters are propelling the rocket that way and as it is moving up, the rocket's mass changes. Mass is the amount of matter in an object, and as the rocket is moving up, fuel is spent so the mass decreases. The force of the boosters however does not decrease, and it is this that causes increasing acceleration. An example of Newton's third law is how the Moon and the Earth interact with each other. While the Earth's gravitational field holds the Moon in its orbit, the Moon's gravity pulls back on the Earth with equal strength (Bortz xx). These laws of motion have been used by others to explain why their ideas would work such as a rocket.

Newton's_ Philosophiae Naturalis Principia Mathematica_, more commonly called _Principia_, included differential and integral calculus, three general laws of motion, universal gravitation, and more (Wiggins). _Principia_ expressed in detail how objects moved on Earth and how planets orbited in space. The most important part of _Principia _is that the book gave a mathematical foundation that could be used to test Newton's ideas. These laws provide the basis for classical mechanics and celestial mechanics. Classical mechanics describes how objects that are not microscopic, such as machine parts, planets, rockets, bullets, etc move. Celestial mechanics is the area of astronomy where Newton's laws of motions are applied to objects in the sky (Celestial). Newton's synthesis helped to explain how the universe works. Newton uses his laws of motion and gravity to explain why celestial bodies, such as the moon and stars, travel in the paths they do (Celestial). The mathematically proven laws of gravitational force and motion are why his synthesis work. Due to Newton's synthesis, questioning of the church and Bible was increased because Newton provided a mathematically proven explanation of the universe, which contradicted what the Church believed, and so others thought that the church may have been wrong about other subjects as well. Newton's discoveries in mechanical physics have helped to form the basis for modern science due to the laws of motion and his synthesis.

Sir Isaac Newton impacted modern science through his discoveries in math and science, which led to more discoveries in those fields and others. Newton's discoveries in math helped impact modern science because they provided mathematical proof that his equations and laws of motion worked. Newton's discoveries in optics helped impact modern science by helping modern organizations such as NASA. Newton's discoveries in physics have impacted science by proving that the church was wrong about some of their beliefs, such as the movement of celestial bodies. This led to increased questioning of various subjects and so more knowledge due to more experimentation. Also, Newton showed that science is enduring and that one topic builds upon another topic, like how his three laws of motion then became the basis for classical and celestial mechanics today. For example, Newton's work in celestial mechanics was modified by Albert Einstein (Celestial). Science advancements not only build on each other, but also expand into other fields as Newton's achievements have shown.

One Scientific discovery often leads to another one, like how Isaac Newton's telescope was an improvement of the reflecting telescope. Although gravity is what most modern people know Sir Isaac Newton for, he had many more achievements besides gravity. Isaac Newton had many important accomplishments in mathematics, including his equations for his laws of physics. Newton's invention of differential calculus allowed him to create his equations. Another accomplishment of Newton was the advancement in the study of optical physics. Newton's most famous accomplishments come in mechanical physics, which he studied after optical physics. All of Newton's work on fields of motion and gravity, including his synthesis, can be found in his _Philosophiae Naturalis Principia Mathematica._ Sir Isaac Newton impacted modern science by setting the basis that science builds upon itself with each discovery leading to a new discovery.

Of Newton's mathematical achievements, he had his most important achievements in equations and theorems. Newton's equations are the mathematical equations for his three laws of motion and the equation for figuring out the force of gravity on an object. Newton's theorem is the binomial theorem. The binomial theorem allows one to take the sum of two integer numbers raised to a power and figure out the answer with only one line of mathematical code. Newton figured out his first law's mathematical equation, ⅀F=0⇒dv/d_t_=0, by observing that planets move in orbit without crashing to the ground, and by watching an apple fall out of a tree. This equation means an object at rest will stay at rest or will continue to stay in motion in a straight line at a constant speed unless an outside force acts upon the object (Allan 33). Newton's equation for the second of the three laws of motion is a=F/_m_. Newton figured out what this laws means by seeing that unequal forces acting on an object created acceleration. What this means is that he observed something like a push would be needed to get an object in motion, otherwise the object would stay at rest continually, which is his first law of motion. Once the push is applied however, the object will accelerate in that direction and at the rate that depends on the object's mass and on the size of the force (Allan 33). Newton's last equation, his equation for the force of gravity on an object is F=G(m1m2/r^2). This equation means that any two objects in the universe attract each other with the resulting force equaling the force of gravity, which equals a force that is directly proportional to the masses times each other and inversely proportional to the distance between the two objects squared. Newton figured out the equation for the gravitational force on an object by observing that if dropped from high enough, two objects even if they do not have the same mass, will hit the ground at the same time. Newton's equations help to prove his laws of motion and the law of universal gravitation by providing mathematical explanation and proof that his laws are correct. With mathematical proof that his equations and ideas work, one can expand upon his equations and apply them to other areas.

Newton's other achievement in mathematics was fluxions and differential calculus. Although he called them "fluxions", they are known today as "derivatives" and are essential in modern calculus (Steele 29). A derivative is the slope of a graph. Calculus "combines arithmetic with geometry and algebra, to compare the rate of change in one thing to the rate of change in another" (Steele 29). There are two types of calculus, differential and integral. While Sir Isaac Newton came up with differential calculus and derivatives, he did not invent integral calculus. Instead, Newton made the discovery of the Fundamental Theorem of Calculus, which states that derivatives and integrals are inverse processes (Calculus). Newton created differential calculus because he wanted to be able to prove the law of universal gravitation, and the strength of mathematics at the time was not strong enough for him to do so. More specifically, Newton "wanted to be able to calculate velocities and accelerations at any point along the path of motion" (Calculus). This takes the form of a curved line and this curved line is known as a derivative. Newton created differential equations as well. A differential equation is "an equation that contains derivatives or instantaneous rates of change" (Calculus). These equations can be used to describe changing phenomena (Calculus), like the three laws of motion. All three laws of motion are differential equations. In "On the Quadrature of Curves", Newton published his findings for derivatives. While Isaac Newton used differential calculus to determine the laws of motion and the law of gravity, it is used today by biologists to determine the rate growth of bacteria when variables such as food and temperature are changed. Another use of differential calculus is credit card companies use differential calculus to figure out the minimum payment due on a credit card statement by considering factors including fluctuating interest rates and a changing available bank balance. Differential calculus can also be used by graphics artists. The graphic artists will use differential calculus to see how different 3-D models will behave when put under swiftly changing conditions. Differential calculus has many uses that contribute to both science and other fields.

Even though his discoveries and accomplishments in mechanical physics are what Isaac Newton is most known for, he had many significant discoveries in optics as well. Optics is a branch of physics that deals with qualities of light, such as its behavior and properties. Included the study of optics is how light interacts with matter and instruments that build or detect light. One of Newton's most important discoveries regarding optics was his work about the spectrum. The spectrum are the "colors into which white light breaks down when passed through a prism" (Allan 47). Newton used a prism and held in sunlight and observed the spectrum. Newton then tried to use another prism to divide up individual colors of the spectrum, but it did not work. Newton's Color Theory is based off of his observation. His color theory states that light that has already been defracted will not change color after being put through a prism again. This led Newton to very important conclusion that "the white light of the sun was a different kind of light from the other colors, because it was a mixture of all of them" (Allan 15). Newton's work on the spectrum affected the development of spectroscopy, which is very important to modern astronomy. Spectroscopy is the science of the interactions that take place between radiation and matter. Spectroscopy can be used to find information about the chemical composition of a star, the temperature of a star, the speed of a star, and how strong a star's magnetic field is, by studying the spectra made by spectra are the individual bands of color from a spectrum. The information about stars is very useful to NASA, the National Aeronautics and Space Administration. Even though Newton did not invent the reflecting telescope, a telescope using mirrors, he greatly improved upon it (Steele 40). Newton's improvement was to use two mirrors. His telescope had a concave mirror at the back, which bounced the rays of light forward to the smaller second mirror halfway up the tube of the telescope. The second mirror reflected the light to an eyepiece, put at the side of telescope tube rather than at the end of the telescope (Allan 27). His telescope magnified objects forty times larger than a refracting telescope, the popular form of the telescope at the time, could. This telescope is now known as a Newtonian telescope. Newton published his findings in his book, _Opticks_. One of the main points of _Opticks_, was that Newton agreed with the theory that light is composed of small particles. The Corpuscular theory is the theory that light travels as a stream of particles that are absorbed by the eye (Light). Also included in _Opticks_ are "discussions of volcanoes, electricity, chemical reactions, capillary action, animal structure, [and God]" (Fara 68). Newton's discoveries in optics, the branch of science that studies light and its properties, impact modern science through spectroscopy, his telescope and his book on the topic, _Opticks_.

Newton's most famous achievements are in mechanical physics. Newton's achievements in this field of science include the three laws of motion, also known as Newton's laws, the law for universal gravitation, and Newton's Synthesis. The first of Newton's three laws states that an object at rest will stay at rest and an object in motion will stay in motion unless an outside unbalanced force is acted upon the object. Newton's second law is that force equals an object's mass times the object acceleration. Newton's third law, "commonly known as the law of action and reaction, states that forces always occur in equal and opposite pairs" (Bortz xx). The law for universal gravitation is that any two objects in the universe attract each other with a force that is directly related to the product of their masses, and inversely related to their distance from each other squared. An example of Newton's first law is if a spaceship were to just drift along in space, it would go on forever and ever, but because the spaceship is acted upon by a planet's gravity, the space ship does not move continuously, instead it moves towards the planet that is acting upon it. An example of Newton's second law is a rocket launching from the launch pad towards space. The object moves up because the rocket's boosters are propelling the rocket that way and as it is moving up, the rocket's mass changes. Mass is the amount of matter in an object, and as the rocket is moving up, fuel is spent so the mass decreases. The force of the boosters however does not decrease, and it is this that causes increasing acceleration. An example of Newton's third law is how the Moon and the Earth interact with each other. While the Earth's gravitational field holds the Moon in its orbit, the Moon's gravity pulls back on the Earth with equal strength (Bortz xx). These laws of motion have been used by others to explain why their ideas would work such as a rocket.

Newton's_ Philosophiae Naturalis Principia Mathematica_, more commonly called _Principia_, included differential and integral calculus, three general laws of motion, universal gravitation, and more (Wiggins). _Principia_ expressed in detail how objects moved on Earth and how planets orbited in space. The most important part of _Principia _is that the book gave a mathematical foundation that could be used to test Newton's ideas. These laws provide the basis for classical mechanics and celestial mechanics. Classical mechanics describes how objects that are not microscopic, such as machine parts, planets, rockets, bullets, etc move. Celestial mechanics is the area of astronomy where Newton's laws of motions are applied to objects in the sky (Celestial). Newton's synthesis helped to explain how the universe works. Newton uses his laws of motion and gravity to explain why celestial bodies, such as the moon and stars, travel in the paths they do (Celestial). The mathematically proven laws of gravitational force and motion are why his synthesis work. Due to Newton's synthesis, questioning of the church and Bible was increased because Newton provided a mathematically proven explanation of the universe, which contradicted what the Church believed, and so others thought that the church may have been wrong about other subjects as well. Newton's discoveries in mechanical physics have helped to form the basis for modern science due to the laws of motion and his synthesis.

Sir Isaac Newton impacted modern science through his discoveries in math and science, which led to more discoveries in those fields and others. Newton's discoveries in math helped impact modern science because they provided mathematical proof that his equations and laws of motion worked. Newton's discoveries in optics helped impact modern science by helping modern organizations such as NASA. Newton's discoveries in physics have impacted science by proving that the church was wrong about some of their beliefs, such as the movement of celestial bodies. This led to increased questioning of various subjects and so more knowledge due to more experimentation. Also, Newton showed that science is enduring and that one topic builds upon another topic, like how his three laws of motion then became the basis for classical and celestial mechanics today. For example, Newton's work in celestial mechanics was modified by Albert Einstein (Celestial). Science advancements not only build on each other, but also expand into other fields as Newton's achievements have shown.


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